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Rudy is a 9-year-old German shorthaired pointer with a regal personality and loving owners who are divorced.

The humans in his life agreed to a shared-custody arrangement: Every two weeks, Rudy goes back and forth between their two homes in Western Massachusetts.

It was an informal deal, worked out with no help from a divorce court. During the breakup, however, Christina Trinchero and her ex-husband brought up the subject of Rudy with their lawyers. "Both of them said: 'Sorry, we can't help you with that. You have to figure it out on your own,'" she recalls.

Almost 80 million US households, or roughly two-thirds, own a pet, according to a 2015 survey from the American Pet Products Association. For every five American couples who get married in a given year, two couples get divorced.

At a time when Americans increasingly are delaying having children, pets can be the most crucial question raised by a divorce or breakup: Who gets custody of the companion animals? Yet courts have little to say on the issue.

Traditionally, the law sees pets as property, no different from a couch or a house plant. That can feel bizarre, given that the average dog or cat has a market value of zero and, in fact, can cost thousands of dollars to feed, walk, and keep healthy. But emotional attachment can turn a beloved pet into a valuable bargaining chip in divorce negotiations.

"People use the animals against one another," says Natalie Reeves, a New York-based divorce lawyer at the firm ToniAnn Grande and an expert on animal law. In bitter divorces, she says, "you take whatever another person loves the most and try to use that against them." That might mean demanding the cat, even if the animal is more attached to your ex.

Judges have a lot of discretion in how they divide property in a divorce. You can strengthen a claim if you can prove that you used your own money - earned before the marriage - to buy the pet or pay for its veterinary bills, Reeves says. Judges are also increasingly considering other factors when splitting up pet-owning couples, such as the best interests of the pets or the families that love them.

When two women were divorcing in 2013, a New York judge agreed to hold a rare hearing on their fight over a dog. "Although Joey the miniature dachshund is not a human being and cannot be treated as such, he is decidedly more than a piece of property," Judge Matthew Cooper wrote.

The ruling was one of the first times a court had ever explained reasons for considering pets as more than property, making it influential even though Judge Cooper is a lower-court judge. The couple eventually settled their dispute out of court.

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Judges, including Cooper, have so far rejected the idea of ordering joint custody arrangements for pets. They also refuse to hold custody hearings for pets in the same way they do for human children.

Couples can hire lawyers to negotiate a private contract, separate from their divorce, to settle questions of pet custody. In practice, Reeves warns, there's no guarantee any court will take these agreement seriously. These deals can also be expensive to negotiate and enforce.

"Although people are very emotionally attached to animals, in the vast majority of cases they can't afford to fight over them," says Joslin Davis, a family lawyer based in Winston-Salem, North Carolina.

We knew the dog was important, and we would make it work no matter what

Debra Vey Voda-Hamilton, a former divorce lawyer, started a firm, Hamilton Law & Mediation, specialising in resolving pet disputes outside of court. She tells her clients: "You hate your ex - I get that - but your pet doesn't."

Dog owners sometimes scale back custody demands when they think through the implications of owning the pet while single, Hamilton says. "They want the dog, but they don't recognise the amount of time and care it takes to take care of the dog."

Agreements reached through mediation can be very detailed. Owners might be required to use groomers or dog walkers to transfer pets between homes, ensuring exes don't have to see or interact with each other.

Rudy's divorced owners didn't go that far. When it's time for the shorthaired pointer to switch homes, they just text or call each other. It works, Trinchero says, because both she and her ex-husband recognise Rudy as their "shared responsibility," even if it's pretty much the only connection they still share.

Trinchero takes Rudy for long walks, her ex takes the dog out pheasant hunting. "He's a member of our family," she says. "We knew the dog was important, and we would make it work no matter what."